In 2018, Kavenagh played Myrtle, working alongside Natalie Dormer and Samara Weaving in the Australian mystery series Picnic at Hanging Rock (2018), and starred as Cindi in six episodes of Romper Stomper,
The same year she appeared as Chloe alongside Jenna Coleman in The Cry (2018), then landed her first film role as Jane Cotter in True History of the Kelly Gang (2019).
In 2020, she appeared as Claudia in My First Summer, and as Daisy Hart for 8 episodes of The Gloaming (2020),
She was cast early on as Elanor "Nori" Brandyfoot in Amazon Prime Video series The Lord of the Rings: The Rings of Power (2022-2024), becoming the first actress to be attached in the high-profile project. She plays the Harfoot daughter of the Brandyfoots, working alongside Lenny Henry and Morfydd Clark.